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<p>We establish the rate of convergence in the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10959_2025_1422_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motion. Our findings extend the known results for the case when the driver is a fractional Brownian motion.</p>

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Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月23日

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  • Kostiantyn Ralchenko,
  • Foad Shokrollahi,
  • Tommi Sottinen

摘要

We establish the rate of convergence in the \(L^1\) L 1 -norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motion. Our findings extend the known results for the case when the driver is a fractional Brownian motion.